I think reverse morals would be good. I wouldn't have gender as part of the name tag, at then general "gender" search will hit it and people searching that are after swaps and benders. role reversal won't work because that's an already established term for when the roles reverse within a relationship, but this tag would be in regards to society as a whole
not upvoting so you can maybe still withdraw (idk if it works that way) but maybe try something like "gender role reversal" or just "role reversals" but that might be too vague